Let \((X, \mathsf {d}, \mathfrak {m})\)  be an \(\operatorname{RCD}(K, N)\)  space with \(k=\dim (X, \mathsf {d}, \mathfrak {m})\) .
We recall some structure results on the reference measure \(\mathfrak {m}\) .
Based on results obtained in [1]}, [2]}, [3]}, [4]}, it is proved in [5]} that the limit
\(\phi (x):=\lim _{r \rightarrow 0^+}\frac{\mathfrak {m}(B_r(x))}{\omega _kr^k}\) 
